<?xml version="1.0" encoding="UTF-8"?><rss xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:atom="http://www.w3.org/2005/Atom" version="2.0"><channel><title><![CDATA[RSS Feed]]></title><description><![CDATA[RSS Feed]]></description><link>http://direct.ecency.com</link><image><url>http://direct.ecency.com/logo512.png</url><title>RSS Feed</title><link>http://direct.ecency.com</link></image><generator>RSS for Node</generator><lastBuildDate>Sun, 12 Apr 2026 16:50:45 GMT</lastBuildDate><atom:link href="http://direct.ecency.com/created/sequences/rss.xml" rel="self" type="application/rss+xml"/><item><title><![CDATA[History of the Fibonacci Sequence and the Golden Ratio]]></title><description><![CDATA[In this video I go over the history of the Fibonacci sequence and Fibonacci numbers as well as their relation to the Golden Ratio and Golden angle, rectangle, and spiral. - summary - playlist - notes #math]]></description><link>http://direct.ecency.com/hive-111030/@mes/history-of-the-fibonacci-sequence-and-the-golden-ratio</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/history-of-the-fibonacci-sequence-and-the-golden-ratio</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 23 Apr 2025 15:34:57 GMT</pubDate><enclosure url="https://images.ecency.com/p/3ejZQFLqXedKXKhURdjx14Sr8NSYZmTdw2HQuQXkeUsn4X1LM6CBB67BuRZfi9A2ZNtn9uArKeq9WKBQ47Y4CC9QALpHczaojwc8MsBxX1XkDxpCr6FBKvNGw2VzJwQ4YRBxk2ThYa3kHKuToGJfsfLq17tJzqBHs6kWh7VNHpAk1YyfYMEsgJEs7N2Ru?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[History of the Fibonacci Sequence and the Golden Ratio]]></title><description><![CDATA[In this video I go over the history of the Fibonacci sequence and Fibonacci numbers as well as their relation to the Golden Ratio and Golden angle, rectangle, and spiral. Although the Fibonacci sequence]]></description><link>http://direct.ecency.com/hive-128780/@mes/mhaunidd</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/mhaunidd</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 23 Apr 2025 05:33:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfKKVdjVhdYcAAo5zoENoGD91i2S2SrpCcqpT7Mw4xjoapLKpkmDinBQKhnPdyjtbvT6559ZNCcA5WbQ?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Exercise 4: Fibonacci's Original Rabbit Reproduction Sequence (and the Golden Ratio)]]></title><description><![CDATA[In this video I go over the first appearance of the famous Fibonacci sequence and show that the limit of the ratio of two consecutive terms is equal to the Golden Ratio. The Italian mathematician Leonardo]]></description><link>http://direct.ecency.com/hive-111030/@mes/exercise-4-fibonaccis-original-rabbit-reproduction-sequence-and-the-golden-ratio</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/exercise-4-fibonaccis-original-rabbit-reproduction-sequence-and-the-golden-ratio</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Sat, 19 Apr 2025 03:53:42 GMT</pubDate><enclosure url="https://images.ecency.com/p/6pu4ZRycQdDVScudzYNpYELDa4hYsxmKLHRL1gYdYaPsV2FdPGpnanPFaYJYH8XCtUgpDQfB1Ecowq8HtmojudMkHbYwkogP8r35PKz5yA4VqabGfSdES6xzRCTgpF5azxNJDyUu7fWHvkwa6aXpc5263xKVd5hQiVyW7nQyMZjKUNju6sax7vixKz27bh1SzCjaf?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Exercise 4: Fibonacci's Original Rabbit Reproduction Sequence (and the Golden Ratio)]]></title><description><![CDATA[In this video I go over the first appearance of the famous Fibonacci sequence and show that the limit of the ratio of two consecutive terms is equal to the Golden Ratio. The Italian mathematician Leonardo]]></description><link>http://direct.ecency.com/hive-128780/@mes/neiphblh</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/neiphblh</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 18 Apr 2025 19:14:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfKKVdjVcMwEmp4kfqXNebygsdky8UQQcSjLfKzJStNnboR59fCTsHG3ydzo4dVVAaSsGx7Cv6QY5xfg?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Exercise 3: Convergent Sequence inside a Continuous Function]]></title><description><![CDATA[In this video I prove Theorem 3, which states that a convergent sequence with limit L can be plugged directly into a continuous function at L, thus obtaining f(L). - summary - playlist - notes #math #sequences]]></description><link>http://direct.ecency.com/hive-111030/@mes/exercise-3-convergent-sequence-inside-a-continuous-function</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/exercise-3-convergent-sequence-inside-a-continuous-function</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 16 Apr 2025 03:25:36 GMT</pubDate><enclosure url="https://images.ecency.com/p/YpihifdXP4WMLzfwe2d1rg9TCZREQLPRYL4YgsSppLMNpvS2ixKzPv8Gknh4UJ8BUSqSN1WkkbS1GjQDsU9uxJmtkW1UZ9UgwAwvaTkyjnvPhGowYqZG6bcQPEHJPtUqgqf52XhrZJVHhGdE93gAjrNWPae6yLKFhZN4QuDn7L5V?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Exercise 3: Convergent Sequence inside a Continuous Function]]></title><description><![CDATA[In this video I prove Theorem 3, which states that a convergent sequence with limit L can be plugged directly into a continuous function at L, thus obtaining f(L). I prove this using the precise definition]]></description><link>http://direct.ecency.com/hive-128780/@mes/mfhyczas</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/mfhyczas</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 16 Apr 2025 03:00:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoVxKVScqqVB6h4EZ5KQyM4pRLaH9bSzkh8gky3LQDh85khF4kbamSwxqNaUtLFRCWPdSfTjZC2?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Exercise 2: If the limit of the absolute values of a sequence is zero, so is the sequence]]></title><description><![CDATA[In this video I prove Theorem 2, which states that if the limit of the absolute values of a sequence is zero, then the sequence itself approaches zero. I solved this using both Squeeze Theorem and the]]></description><link>http://direct.ecency.com/hive-111030/@mes/exercise-2-if-the-limit-of-the-absolute-values-of-a-sequence-is-zero-so-is-the-sequence</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/exercise-2-if-the-limit-of-the-absolute-values-of-a-sequence-is-zero-so-is-the-sequence</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 14 Apr 2025 17:40:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/YpihifdXP4WMLzfwe2d1rg9TCZREQLPRYL4YgsSppLMNpvS2ixKzPv8FPStnzawaxvbNC8Vzwpiw54H5wssaRrM7yMgS9cwQ9dq454XnbT95h2ErDmbmdijCh1eSJziVw3LyFdzvgvEwGxAhZPJ3YGcW33tVZFqx2ETFHRYaT7AF?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Exercise 2: If the limit of the absolute values of a sequence is zero, so is the sequence]]></title><description><![CDATA[In this video I prove Theorem 2, which states that if the limit of the absolute values of a sequence is zero, then the sequence itself approaches zero. I solved this using both Squeeze Theorem and the]]></description><link>http://direct.ecency.com/hive-128780/@mes/sgnogped</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/sgnogped</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 14 Apr 2025 16:46:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoVxKxJkNCNjFvGmgBX47GJP4f3NEM6be81vUQrPiCtMdMJM3zJ2ytBegnEApeVy3UTjjM3rTtr?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Exercise 1: Limit of a Sequence and the Golden Ratio (Minus 1)]]></title><description><![CDATA[In this video I show that the limit of a sequence is the same if the sequence was shifted by 1 term. I use this fact to solve for the limit of a recursive sequence by plugging in the limit into the recursion]]></description><link>http://direct.ecency.com/hive-111030/@mes/exercise-1-limit-of-a-sequence-and-the-golden-ratio-minus-1</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/exercise-1-limit-of-a-sequence-and-the-golden-ratio-minus-1</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 14 Apr 2025 04:58:18 GMT</pubDate><enclosure url="https://images.ecency.com/p/4bEjbgCbFMvA8T33kGvF6kHce4BTcm88Pv5WXm8EBoMz3u29V4LrZvMEwg8eVJ9osbigz59aF5YU4hgWFyaRurY5BxjCBBUNehsYsAE59jkA3wZkYSg4GoY3TzvM3mzLQA6Ywd4dtb6xNgoaFKKg9KMH6fKzwGBRPhGmXAFkwuntYMkG8f?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Exercise 1: Limit of a Sequence and the Golden Ratio (Minus 1)]]></title><description><![CDATA[In this video I show that the limit of a sequence is the same if the sequence was shifted by 1 term. I use this fact to solve for the limit of a recursive sequence by plugging in the limit into the recursion]]></description><link>http://direct.ecency.com/hive-128780/@mes/verunqmp</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/verunqmp</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 14 Apr 2025 04:29:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoVvUQxoZpqYt9uEyQpYT1AoKFhzdSqQTdStgC3PTPZjLBXGG6YtXoqybE3fABXdWzs1TVmbVhY?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Bounded Sequences, Completeness Axiom, and the Monotonic Sequence Theorem]]></title><description><![CDATA[In this video I first go over the definition of bounded sequences, then discuss the completeness axiom in number theory and how it is used to proof the monotonic sequence theorem. - summary - playlist]]></description><link>http://direct.ecency.com/hive-111030/@mes/bounded-sequences-completeness-axiom-and-the-monotonic-sequence-theorem</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/bounded-sequences-completeness-axiom-and-the-monotonic-sequence-theorem</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 11 Apr 2025 17:34:45 GMT</pubDate><enclosure url="https://images.ecency.com/p/2Snpznz7rwiEdJnR5Rzb8HdpDtLFUR7vWRCLde6bYWedt2juHpQ1aLpvzjdaZjnhg33xgd2Qbgs4KEicAXCXPZ9Spk4KeHevX2H3mfPCtgHC31S1CUmhDcrkwhezmCeobm4y1i5eBwUb5H99DuzjGZ4TUWqFcjN7YRCXUysDM1NbDfmPy4UccmDa7QQdbDGS22G78vMEQwwSw1KyjfD?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Bounded Sequences, Completeness Axiom, and the Monotonic Sequence Theorem]]></title><description><![CDATA[In this video I first go over the definition of bounded sequences, then discuss the completeness axiom in number theory and how it is used to proof the monotonic sequence theorem. A sequence is bounded]]></description><link>http://direct.ecency.com/hive-128780/@mes/msxghnik</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/msxghnik</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 11 Apr 2025 17:11:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoVxbZQBgpagBNwKBEab89zWKKfnqrSinwaLRmHdnfKw8jTCJf6b7W5crkki2bYxtvsNWd2Koev?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Using Mathematical Induction to find the Limit of a Recursive Sequence]]></title><description><![CDATA[In this video I go over an example of a sequence that is defined by a recurrence relationship, and then use mathematical induction to prove it is increasing, bounded, thus convergent, and finally its actual]]></description><link>http://direct.ecency.com/hive-111030/@mes/using-mathematical-induction-to-find-the-limit-of-a-recursive-sequence</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/using-mathematical-induction-to-find-the-limit-of-a-recursive-sequence</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 08 Apr 2025 17:09:42 GMT</pubDate><enclosure url="https://images.ecency.com/p/ATHztMY7eTanRk3GJThkibYnoPqfpCahxXDEzQqunddesTewXm5qdPXdsLjRXtjZULbbE6ZkTtCCA2JdGepAq57HT5YFbuNTieBEaCw2WiMrQACJ3Soqtw42u7CWSxh31iF3xLDVdfAsQ1e83to9WVvcJa6bNEvdtqoAmFSvfdD4LXc7qM9wKrPxk1F1r4i4k4hW8aoKB5HEpUFauZjduimM?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Using Mathematical Induction to find the Limit of a Recursive Sequence]]></title><description><![CDATA[In this video I go over an example of a sequence that is defined by a recurrence relationship, and then use mathematical induction to prove it is increasing, bounded, thus convergent, and finally its actual]]></description><link>http://direct.ecency.com/hive-128780/@mes/yqdsumlm</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/yqdsumlm</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 08 Apr 2025 16:56:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoW1Vpwk2eBg4qkjrmotVmE5kM3kjWuvQ2azXVZfSsf9TM92KaS3n8YbV7JeRjspaVA5tUETuiN?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Monotonic Sequences and Examples]]></title><description><![CDATA[In this video I go over the definition of increasing and decreasing sequences, which are thus denoted as Monotonic. - summary - playlist - notes]]></description><link>http://direct.ecency.com/hive-111030/@mes/monotonic-sequences-and-examples</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/monotonic-sequences-and-examples</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 07 Apr 2025 16:39:21 GMT</pubDate><enclosure url="https://images.ecency.com/p/2dk2RRM2dZ8gG2NWUA1Si8uQVuafUvSygay9VsRhqFpPwzrjmHrbE6xQCSpfkEB5uEFWB57cDmnnj58LCyXN87kusqfAytSaiwYVNuLfRP72EZtHjkuKUrWQyZHEcoXKiRGkqYCvf9g9p2LkEnM8encJC3eBF6xxRcbyT1qZmy?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Monotonic Sequences and Examples]]></title><description><![CDATA[In this video I go over the definition of increasing and decreasing sequences, which are thus denoted as Monotonic. An increasing sequence has each consecutive term bigger than the previous, while a decreasing]]></description><link>http://direct.ecency.com/hive-128780/@mes/pjjirnvh</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/pjjirnvh</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 07 Apr 2025 16:24:12 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoVyPfEDF6Ewekr77AJEq7ZPW2zeN1nv6mzbmxPSZ45g1vWRAxNLuG8gUD6HzhHbr5cTopgYdup?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Creating Graphs of Sequences]]></title><description><![CDATA[In this video I discuss how to graph sequences manually as well as using Desmos online graphing calculator. - summary - playlist - notes]]></description><link>http://direct.ecency.com/hive-111030/@mes/creating-graphs-of-sequences</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/creating-graphs-of-sequences</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 01 Apr 2025 22:10:57 GMT</pubDate><enclosure url="https://images.ecency.com/p/5s4dzRwnVbzGM3JdyYKz6jx9fFPTMbZhYMErUJH1tgUBpmQC5hkUcvUXrGbWX6LdEXifENmjDF5NhmYsj5W2g4MrMTZXcfE3cZVCWHGg8HqEq8Rxg5WmDT6nftQ1GMNUBkgAs1c2X9LAxkirDkG1g2wqgetewx51it5L3kK?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Creating Graphs of Sequences]]></title><description><![CDATA[In this video I discuss how to graph sequences manually as well as using Desmos online graphing calculator. I also go over an example on finding the values of r in r^n that are convergent and plot them]]></description><link>http://direct.ecency.com/hive-128780/@mes/ygwyzrde</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/ygwyzrde</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 01 Apr 2025 18:56:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoVxWi2m75uZsUbyorToztjuyQrCucRevjdW64MhCj8LkzDNHPbHkSNDrGvP7Fcpb6oCsQMXir2?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Plugging a Sequence into a Function and Examples]]></title><description><![CDATA[In this video I go over Theorem 3, which states that if a sequence has a limit, then plugging it into a continuous function at that limit is the same as plugging in the limit. - summary - playlist - notes]]></description><link>http://direct.ecency.com/hive-128780/@mes/plugging-a-sequence-into-a-function-and-examples</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/plugging-a-sequence-into-a-function-and-examples</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 31 Mar 2025 22:38:27 GMT</pubDate><enclosure url="https://images.ecency.com/p/BgxWBRxjvNhnbM9Dipe2ZCkExrPnrSh6XZgCn7b4eotkeq8gxrG39uVxZMJ2S9m2gXY9HLKFvzbavpNtpzJuYmeBSGAzcjAvCvZpk4D6u8kHQM5qSpKfX81aKZMmHY5bgUqAym9QPq6mDeoMViWknizTVS1kbUurCPSVCqm5JvZ9hrP?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Examples on Limits of Sequences]]></title><description><![CDATA[In this video I go over 4 examples on the limits of sequences and on determining if the limits exists or the sequence diverges. - summary - playlist - notes]]></description><link>http://direct.ecency.com/hive-111030/@mes/examples-on-limits-of-sequences</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/examples-on-limits-of-sequences</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 31 Mar 2025 03:29:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/7b4bio5hobgskW8qdJJeDjrJHTiT5uLGk5BQErotAHijnZQZsvzoyRZ1qfoZzzn6rPUqgYJzqJ9NG3RvidjHzyTes7fsnH5DZSHCYd2GLryRjUB7Qdaf1aK3Z67nwBKFk6rQpJA6gP2mCLGaqdwbBsQBspj1?format=match&amp;mode=fit" length="0" type="false"/></item></channel></rss>